Four times the sum of the number of reds and blue exceeded 3 times the number of whites by 3. Five times the sum of the number of blues and whites exceeded 8 times the number of reds by 13. If there were 5 more whites than blues, how many of each color were there?

Answer 1

just put the clues into symbols:

4(r+b) = 3w+3
5(b+w) = 8r+13
w = b+5

now substitute for w in the 1st two equations:

4(r+b) = 3(b+5)+3
5(b+b+5) = 8r+13
or,
4r + b = 18
8r - 10b = 12

8r - 10(18-4r) = 12
48r = 192
r = 4
so, b=2 and w=7